The angular momentum carried off by electromagnetic or gravitational waves is evaluated by computing the torque exerted by the radiation on the emitting system. The lowest order secular effect in the electromagnetic case is proportional to the vector product of the first and second time derivatives of the electric dipole. In the gravitational case, the lowest order term is proportional to the antisymmetrized product of the second and third time derivatives of the mass quadrupole.
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Morgan et al. (1963) studied this question.
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